37 degrees plus m mus equal 90 degrees; therefore, the equation that m must satisfy is
[tex]m+37=90[/tex]subtracting 37 from both sides of the equation gives us
[tex]m=90-37[/tex][tex]\textcolor{#FF7968}{\therefore m=53^o}[/tex]I need help to find x and could you explain it also please
At a fundraiser hosted by a local restaurant, customers can pay as much or as little as they like for a meal, as long as they pay at least $1. any profits are donated to a local charity. one evening, the mean (average) price paid per customer was $55. one more customer walked in and paid $70 for a meal, bringing the average up to $56. what is the highest possible price that a customer could have paid for their meal that evening? do you think the amounts in your solution are reasonable.
in your solution are reasonable for this situation?
The highest possible price that a customer could have paid for their meal that evening exists $ 757. Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.
How to estimate the highest possible price that a customer could have paid for their meal that evening?When determining the mean (average) of a group of values, we add up the values in the group and divide that total by the number of values in the group. As a result, the average of the set's values divided by the total number of values is equal to the set's values' sum.
Let n represent how many people were in the store that evening. Thus, a total of 56n was paid that evening by all customers. The bill for the last customer's meal was $70.00. There were (n-1) customers who had already paid a total of (56n-70) dollars before this one arrived. The average cost per customer at that time was $55 dollars.
From the above information, we get
[tex]$\frac{56 n-70}{n-1} &=55 \\[/tex]
simplifying the above equation, we get
56n - 70 = 55(n - 1)
56n - 70 = 55n - 55
n = 15
Since n = 15, it follows that there were 15 customers that evening, and the total amount paid by all customers stood therefore 56 n = 56(15) = 840 dollars.
To estimate the highest possible price that a customer could have paid for their meal that evening, we will assume that 13 of the customers paid the lowest possible price of $ 1. Then the remaining customer would have paid 840 - 13 × 1 - 70 = 757 dollars.
Therefore, the highest possible price that a customer could have paid for their meal that evening exists $ 757.
Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.
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Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? Last week, he made $ in commission.
EXPLANATION
Let's see the facts:
%Earns= 13% commission/week
Last week sold = $7,500
In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:
$Earns = 0.13 (decimal form)*$7,500
Earns = $975
Last week, he made $975 in commission.
If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year
use the distributive property to solve 4 × ( 10 + 7)
Given the expression:
[tex]4\ast(10+7)[/tex]Let's solve the expression using distributive property.
To use distributive property, distribute the term ouside the parentheses to the terms in the parentheses.
Apply distributive property:
[tex]a\ast(b+c)=ab+ac[/tex]Distribute 4 to the values inside the parentheses:
[tex]\begin{gathered} 4\ast(10+7) \\ \\ =4(10)+4(7) \\ \\ =40+28 \\ \\ =68 \end{gathered}[/tex]ANSWER:
68
If John Carlo has 4 times as many nickels as quarters and they have a combined value of 270 cents, how many of each coin does he have?
There 6 quarters and 24 nickels of each coins that John Carlo has.
How to calculate for the number of each coins.There are 5 cents in a nickel and 25 cents in a quarter. Let us represent the number of quarters as x so that the number of nickels that John Carlo has will be 4x.
Thus, 4x(5 cents) + x(25 cents) = 270 cents
20x cents + 25x cents = 270 cents
45x cents = 270 cents
divide through by 45
x = 270/45
x = 6
and thus there are 4(6) = 24 nickels.
Therefore, John Carlo has 6 quarters and 24 nickels each of coins.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
which of the following value are solutions to the inequality -5>6x+9
Given:
The inequality is,
[tex]-5>6x+9[/tex]Required:
To choose the correct value for the given inequality.
Explanation:
Consider the given inequality,
[tex]-5>6x+9[/tex]Consider the first option, 6
Put x=6 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times6+9 \\ -5>36+9 \\ -5>45 \end{gathered}[/tex]Clearly the statement is false.
Now consider the next option, 4
Put x=4 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times4+9 \\ -5>24+9 \\ -5>33 \end{gathered}[/tex]Clearly the statement is false.
Now consider the next option, 0
Put x=0 in to the given inequality, we get
[tex]\begin{gathered} -5>6\times0+9 \\ -5>9 \end{gathered}[/tex]Clearly the statement is false.
Final Answer:
There is no values in the given options .
The next number in the arithmetic sequence 10, 23, 36, ___ is:
Answer:
49
Step-by-step explanation:
10 to 23 is 13, and 23 to 36 is 13. so you just add 13 to 36 to get 49
A solution to a system of linear equations in two variables is an ordered pair that.
A solution to a system of linear equations in two variables is an ordered pair that makes BOTH equations true.
When is the system of equations is said to be consistent?
If there is at least one combination of values for the unknowns that satisfies each equation in the system—that is, makes each equation hold true as an identity—then a system of equations, whether linear or nonlinear, is said to be consistent.
When is the system of equations is said to be non-consistent?
If there isn't a set of values for the unknowns that solves every equation, then the system of equations is said to be inconsistent.
Ex: Consider a system of linear equations:
x+3y=6
x=-3y+6 …..(1)
2x+8y= -12 …..(2)
Substitute equation (1) in (2)
2(-3y+6)+8y=-12
-6y+12+8y=-12
2y=-24
y=-12 ….(3)
Substitute equation (3) in (1)
x+3(-12)=6
x-36=6
x=42
Here, the order pair (x,y)=(42,-12) is the solution of the given linear equations and satisfy equations (1) and (2)
> 42+3(-12) = 42-36 .....From (1)
= 6 = RHS
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Zachary is paying his dad back for the money he borrowed to pay for a car repair. The amount that he owes his dad is shown in the graph
Answer:
so you need to divide this and turn it into a coefficient for the answer
Step-by-step explanation:
An arithmetic sequence has the following
properties:
i) Its 6th term is 15.
ii) Its 9th term is three times the 2nd term.
Find the 100th term of this sequence.
The 100th term of the arithmetic sequence is 203.
Let the first term of the arithmetic sequence be a and the common difference be d.
The general term of the sequence is given by
[tex]T_{n} = a + (n-1)d[/tex]
It is given that the 6th term is 15, we have :
[tex]T_{6} = a +5d[/tex]
a + 5d = 15......equation(1)
It is given that the 9th term is three times the 2nd term, we have :
[tex]T_{9} = 3*T_{2} \\a + 8d = 3(a +d)\\a + 8d = 3a +3d\\a -3a = 3d -8d = -5d\\-2a = -5d\\2a = 5d\\a = \frac{5d}{2}[/tex]
Putting this value in equation(1)
[tex]\frac{5d}{2} + 5d = 15 \\\\5d + 10d = 30\\15d= 30\\d = \frac{30}{15} = 2[/tex]
a = 5*2/2 = 5
Hence, the first term is 5 and the common difference is 2.
Now, evaluating the 100th term of the sequence, we have :
[tex]T_{n} = a +(n-1)d\\T_{100} = a +99d\\T_{100} = 5 +99*2 = 5 +198 = 203[/tex]
Hence, the 100th term of the arithmetic sequence is 203.
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can you help me on this?
Answer:
The answer is run because the line is going down.
Step-by-step explanation:
Write the system of linear equations represented by the augmented matrix. (Use variables x, y, and z, if applicable.)1 - 1 21-30 1 -1 50 0 1-5Use back-substitution to solve the system.(x, y, z) =
The augmented matrix represents the following system of linear equations:
[tex]\begin{gathered} x-y+2z=-3 \\ y-z=5 \\ z=-5 \end{gathered}[/tex]Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:
[tex]\begin{gathered} y-z=5 \\ y-(-5)=5 \\ y+5=5 \\ y=5-5 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} x-y+2z=-3 \\ x-0+2(-5)=-3 \\ x-10=-3 \\ x=-3+10 \\ x=7 \end{gathered}[/tex]The solution of the system is (x, y, z)=(7, 0, -5)
Bill flip a coin and roll a dice independent or dependent
Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.
Independent Events which we learn about here.
Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.
AnswerIndependent
In Mrs. Stone's class, 18 out of 30 student turned in their homework on time. What percent of the class turned their homework in on time?
4x+2y=2 and y=-3x+2 slove the system of equations
The solution of the given system of equations is x =1 and y = -1.
What is a system of equations?In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Given is a system of equations; 4x+2y=2 and y=-3x+2
Solving the equation by substitution, we get,
4x+2(-3x+2) = 2
4x-6x-4 = 2
-2x+4 = 2
-2x = -2
x = 1
Put x = 1 in any of the given equation,
y = -3*1+2
y = -3+2
y = -1
Hence, The solution of the given system of equations is x =1 and y = -1.
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Alicia has at most $196 to buy a new baseball gloves and a new baseball hat. What inequality can represent this?
Alicia has at most $196 this means that her amount of money is less or equal than $196, we can express this as an inequality, like this:
[tex]\text{y}\leq\text{ \$}196-x[/tex]Where x represents the cost associated with the hat and the gloves and y is the money that left after the purchase of these articles
Subject :- Optional Mathematics
Topic :- Fraction
The value of x is 0.94 or 3.34 with the functions given.
The function is given as:
f = (x, 4 x - 17)
g = (x, (2 x + 8) / 5)
We get that:
g⁻¹ (x) = (2 x + 8) / 5
f o f (x)
= f (f (x))
= (4x [ 4x - 17] - 17)
= 16 x² - 68 x - 17
ATQ:
16 x² - 68 x - 17 = (2 x + 8) / 5
80 x² - 340 x - 85 = 2 x + 8
80 x² - 342 x - 93 = 0
Solving the equation:
D = b² - 4 ac
D = (-342)² - 4 (80) (-93)
D = 36681
x = (342 ± √36681) / 2(80)
x = (342 ± 191.52) / 160
x = 0.94 or x = 3.34
Therefore, the value of x is 0.94 or 3.34 with the functions given.
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Which of the following equations is equivalent to 2/3x- 1/2Y=6
O4x - 3y = 36
2x - y = 36
O 2x - y = 6
Answer:
4x - 3y = 36
Step-by-step explanation:
⅔x-½y=6
just multiply both sides by the LCM which is 6
6×⅔x-6×½y=6×6
4x-3y=36
Hello! Having a little trouble on this question, thanks for your help!
The graph of the function:
[tex]g(x)=ln(4-x)[/tex]Can be obtained by using the parent function:
[tex]f(x)=ln(x)[/tex]Whose graph is shown below:
We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:
[tex]f(-x)=ln(-x)[/tex]And the graph is:
Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:
[tex]g(x)=f(4-x)=ln(4-x)[/tex]The graph is shifted 4 units to the right as shown:
16. Describe, step-by-step how to find the slope of a line through two points.
Answer:
1. find the 2 points and determine their coordinates.
2. determine the difference in the rise or y-coordinates.
3. determine the difference in the run or x-coordinates.
4. place the rise over the run and divide to find slope
One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 5 or a Club. Note that the ace is considered a low card.The probability that the card selected is less than 5 or a club is.(Type an integer or a simplified fraction.)
The total number of cards in a deck of cards is: 52
The total number of club cards is: 13
The total number of cards that less than 5 is: 8.
The probability of selecting a club card is,
[tex]\begin{gathered} P(Club)=\frac{Total\text{ number of club cards}}{\text{Total number of cards}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of selecting a card that is less than five is,
[tex]\begin{gathered} P(card<5)=\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The total number of club card that is less than 5 is 3.
The probability of selecting a club card and a card that is less than 5 is,
[tex]P\text{ (club and less than 5)}=\frac{3}{52}[/tex]The probability of selecting a card that is a club or less than 5 is,
[tex]\begin{gathered} P\text{ (Club or less than5)}=P(Club)+P\text{(card less than 5)-P(Club and less than 5)} \\ =\frac{1}{4}+\frac{2}{13}-\frac{3}{52} \\ =\frac{21}{52}-\frac{3}{52} \\ =\frac{9}{26} \end{gathered}[/tex]Thus, the probability of selecting a club card or card that is less than 5 is 9/26.
Which ordered pair is a solution for this system of linear inequalities?
2x + 3y < 12
3x - 2y ≥ 18
A. (5,0)
B. (3,-1)
C. (-1,3)
D. (4,-9)
The ordered pair that is a solution for the inequality 2x + 3y < 12 and
3x - 2y ≥ 18 is
D. (4,-9)How to find the solutionThe solution is sought by substituting to each of the pair to the equation and comparing the answers
for D. (4,-9)
2 * 4 + 3 * -9 < 12
-19 < 12 correct
3x - 2y ≥ 18
3 * 4 - 2 * -9 ≥ 18
30 ≥ 18 correct
This proves that option D is the correct option
trying for A. (5,0)
2 * 5 + 3 * 5 < 12
25 < 12 incorrect
3x - 2y ≥ 18
3 * 5 - 2 * 0 ≥ 18
15 ≥ 18 incorrect
trying for B. (3,-1)
2 * 3 + 3 * -1 < 12
3 < 12 correct
3x - 2y ≥ 18
3 * 3 - 2 * -1 ≥ 18
11 ≥ 18 incorrect
When any part is incorrect the pair is not a solution
trying for C. (-1,3)
2 * -1 + 3 * 3 < 12
7 < 12 correct
3x - 2y ≥ 18
3 * -1 - 2 * 3 ≥ 18
-9 ≥ 18 incorrect
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Select the correct answer.
Solve the system of equations.
y=x-5
y=x-5x+3
O A. (4,-3) and (2,-1)
О в.
(4,-1) and (2,-3)
O C.
(-4,-9) and (-2,-7)
O D.
(4,-9) and (2,-7)
The value of x is -2 and the value of y is -7. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equations are y = x - 5 and y = 5x + 3. The value of x and y will be calculated by solving the equations,
y=x-5
y=5x+3
x -5 = 5x + 3
-4x = 8
x = -2
The value of y will be calculated as,
y = x - 5
y = -2 - 5
y = -7
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i need helppp!!!!!!!!
Answer:
5
Step-by-step explanation:
y=x+5 cuz it works out for everything
Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, with a replacement.
Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.
The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is
[tex]\frac{4}{52}=\frac{1}{13}[/tex]Since the cards are replaced, it is the same probability of getting an Ace on each draw.
Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is
[tex]\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}=\frac{1}{13^4}=\frac{1}{28561}=0.00003501277\ldots[/tex]79 plus 34???????????????
EXPLANATION
The sum of 79 and 34 is
[tex]79+34=113[/tex]Answer: 113
To rent a moving truck for the day, it costs $75 plus $1.50 for each mile, m, driven. Which expression represents the cost, in dollars, to rent the moving truck?
The expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to represent the total cost will be:
The truck costs $75.And an extra $1.50 for every mile.The expression that gives the total cost.
Let, the number of miles are 'n' and the total cost be 'C'.
Now,
1.50n + 75 = C
Therefore, the expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.
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Hi I need a fit of help with this question!
Explanation
The unit rate os obtained as shown as follows:
[tex]\text{Unit rate = }\frac{change\text{ in dollars}}{\text{change in hours}}[/tex][tex]\text{Unit rate= }\frac{17\text{dollars}}{\text{hour}}=\text{ 17\$/h}[/tex]Answer is A. The unit rate is equal to $17.
Lu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.
$556.35
$648.35
$660.32
$721.31
Answer:
The total deposit is $721.31.
Step-by-step explanation: